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Atlas › Integer Profiles › Node 46,320,100

46,320,100

22 × 52 × 19 × 24379
Abundant Even Composite

46,320,100 factors as 2^2 × 5^2 × 19 × 24379. Its 36 positive divisors give a proper-divisor sum of 59,489,100, so this integer is abundant. The Collatz stopping time is 235 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 19 × 24379
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 105,809,200
Proper Divisor Sum 59,489,100
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #46320089 ← → #46320101

Radix Representation

Decimal 46320100
Binary 10110000101100100111100100 (26 bits)
Octal 0o260544744
Hexadecimal 0x2C2C9E4

Divisor Catalog (36)

1 2 4 5 10 19 20 25 38 50 76 95 100 190 380 475 950 1,900 24,379 48,758 97,516 121,895 243,790 463,201 487,580 609,475 926,402 1,218,950 1,852,804 2,316,005 2,437,900 4,632,010 9,264,020 11,580,025 23,160,050 46,320,100

Collatz Trajectory (235 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

46,320,100 23,160,050 11,580,025 34,740,076 17,370,038 8,685,019 26,055,058 13,027,529 39,082,588 19,541,294 9,770,647 29,311,942 14,655,971 43,967,914 21,983,957 65,951,872 32,975,936 16,487,968 8,243,984 4,121,992 2,060,996 1,030,498 515,249 1,545,748 772,874 386,437 1,159,312 579,656 289,828 144,914 72,457 217,372 108,686 54,343 163,030 81,515 244,546 122,273 366,820 183,410 91,705 275,116 137,558 68,779 206,338 103,169 309,508 154,754 77,377 232,132 116,066 58,033 174,100 87,050 43,525 130,576 65,288 32,644 16,322 8,161

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